Unsteady free convective boundary-layer flow near a stagnation point in a heat-generating porous medium

Abstract

The free convection boundary-layer flow near a stagnation point in a porous medium is considered when there is local heat generation at a rate proportional to (T − T _∞)^p, (p ≥ 1), where T is the fluid temperature and T _∞ the ambient temperature. Two cases are treated, when the surface is thermally insulated and when heat is supplied at a constant (dimensionless) rate h _s from the boundary. If h _s = 0 the solution approaches a nontrivial steady state for time t large in which the local heating has a significant effect when p ≤ 2. For p > 2 the effects of the local heating become increasingly less important and the solution dies away, with the surface temperature being of O(t ⁻¹) for t large. When h _s > 0 and there is heat input from the surface, the solution for p ≤ 2 again approaches a nontrivial steady state for t large and all h _s . For p > 2 there is a critical value h _s,crit (dependent on the exponent p) of h _s such that the solution still approaches a nontrivial steady state if h _s < h _s,crit. For h _s > h _s,crit a singularity develops in the solution at a finite time, the nature of which is analysed.